Parallel Graph Algorithms list ranking connectivity tree compression
- Slides: 14
Parallel Graph Algorithms • • • list ranking connectivity tree compression bip. graph testing max. matching in bip. graph • convexity of bip. graphs (01 -property) • planarity testing Frank Dehne CGM complexity: • O(log p) rounds • n/p > p • O(n/p) local comp. per round www. dehne. net
List Ranking Frank Dehne www. dehne. net
r-Ruling Set O(N/P) "selected" nodes with distance O(r) between consecutive nodes. Frank Dehne www. dehne. net
List Ranking Algorithm • Determine an O(p 2)-ruling set. • Execute O(log p) rounds of pointer jumping. • Compress ruling set into one processor and perform list ranking sequentially. • Compute ranks of all other nodes. Frank Dehne www. dehne. net
Rand. List Ranking Algorithm • Select random n/p elements as ruling set and then improve. . . CGM complexity: • O(log p log n) rounds • n/p > p • O(n/p) local comp. per round Frank Dehne www. dehne. net
Det. List Ranking Algorithm • A CGM adaptation of deterministic coin tossing. . . CGM complexity: • O(log p) rounds • n/p > p • O(n/p) local comp. per round Frank Dehne www. dehne. net
Rand. List Ranking Frank Dehne www. dehne. net
Det. List Ranking Frank Dehne www. dehne. net
CGM Graph Algorithm Library • • • list ranking connectivity tree compression bip. graph testing max. matching in bip. graph • convexity of bip. graphs (01 -property) • planarity testing. . . Frank Dehne CGMlib CGM utilities CGMgraph CGM graph algorithms Download and documentation at http: //cgm. dehne. net www. dehne. net
Library Design Frank Dehne www. dehne. net
Library Design Frank Dehne www. dehne. net
Connected Components Frank Dehne www. dehne. net
Bipartite Graph Detection Frank Dehne www. dehne. net
Frank Dehne www. dehne. net